Find a flaw in the following "proof' that a relation on a set S is reflexive if it is

Chapter 9, Problem 9.22

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Find a flaw in the following "proof' that a relation on a set S is reflexive if it is both symmetricand transitive: Let XES. From x ~ y, by symmetry, we have y ~ x. By transitivity, x ~ yand y ~ x imply x ~ x. Therefore, ~ is reflexive.

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